Converting Linear Equations

The slope-intercept form is given by the equation $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

To convert from point-slope form $$y - y_1 = m(x - x_1)$$ to slope-intercept form, solve for $$y$$ to get $$y = mx + (y_1 - mx_1)$$ .

The standard form is given by the equation $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers, and $$A$$ should be non-negative.

$$y = \frac{1}{3}x + 9$$ .

$$x - 3y = -27$$ .

$$y = -3x + 9$$ .

$$y = 3x + 14$$ .

The slope $$m$$ is calculated as $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ .

$$4x + y = 5$$ .

The slope represents the rate of change of $$y$$ with respect to $$x$$ ; it indicates how steep the line is.